How do I stack triangles into a bigger triangle with array modifier?
I don't think there is a way to do this with modifiers alone, apart form applying them and edit the result manually.
You can Apply your modifiers (from the top down), then go into Edit mode and select and delete the parts you don't want.
Alternatively you could download, install and activate the Array Tools add-on. It allows for a variation for each new row (like -1 triangle). The add-on however does not work with modifiers and every triangle would be a separate object.
Example of the add-on: